# Tag Archives: fundamental subspaces

## Linear Algebra and Its Applications, Exercise 3.4.15

Exercise 3.4.15. Given the matrix find the orthonormal vectors and that span the column space of . Next find the vector that completes the orthonormal set, and describe the subspace of of which is an element. Finally, for find the … Continue reading

## Linear Algebra and Its Applications, Review Exercise 2.27

Review exercise 2.27. Find bases for each of the following matrices: Answer: If we put in echelon form (by exchanging rows 3 and 4) the resulting matrix would have pivots in columns 1, 2, and 4. Columns 1, 2, and … Continue reading

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## Linear Algebra and Its Applications, Exercise 2.4.3

Exercise 2.4.3. For each of the two matrices below give the dimension and find a basis for each of their four subspaces: Answer: We first consider the column spaces and . The matrix has two pivots and therefore rank ; … Continue reading

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## Linear Algebra and Its Applications, Exercise 2.4.2

Exercise 2.4.2. For each of the two matrices below give the dimension and find a basis for each of their four subspaces: Answer: The echelon matrix has only a single pivot, in the second column. As discussed on page 93, … Continue reading

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